Finite Group Databasebeta

← #478×D47 #20253141

Subgroups — #478×D47 #20253141

Order 6016.

448 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D47C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic
3#15689426C211yesmaximal, characteristic, complemented
4#15689425C211yesmaximal, characteristic, complemented
5#15689424C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689422C211yesmaximal, characteristic, complemented
8#15689421C211yesmaximal, characteristic, complemented
9#15689420C211yesmaximal, characteristic, complemented
10#107×D47C211yesmaximal, characteristic, complemented
11#106×D47C211yesmaximal, characteristic, complemented
12C4⋊C8×D47C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic
14#102×D47C211yesmaximal, characteristic
15C47×#478C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C22×C4×D47—21no—
18C2×C8×D47C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094016C2211yescharacteristic, complemented
21#13094015C2211yescharacteristic, complemented
22#13094015C2211yescharacteristic, complemented
23#13094014—21no—
24#13094014—21no—
25C4×D188C2211yescharacteristic
26D4×Dic47C2211yescharacteristic
27#13093986C2211yescharacteristic
28C4×C22⋊D47—21no—
29(C22⋊D47)⋊C4—21no—
30C4⋊C4×D47—21no—
31C4⋊C4×D47—21no—
32C4⋊C4×D47C2211yescharacteristic
33C4⋊C4×D47C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35C22⋊C4×D47—21no—
36C42×D47C2211yescharacteristic
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43C4⋊(C47⋊C8)C2211yescharacteristic, complemented
44Dic47⋊C8C2211yescharacteristic, complemented
45Dic47⋊C8C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52#125×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64D4×D47—22no—
65D4×D47Q814yes—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—44no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C8×D47—22no—
106C8×D47—22no—
107C23×C47—21no—
108C22×D47—21no—
109C22×D47—24no—
110C22×D47—42no—
111C22×D47—42no—
112C22×D47C2×D411yescharacteristic
113D4×C47—21no—
114D4×C47C2×Q812yes—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—42no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—24no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—42no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188C2×Q812yes—
132C4×D47—22no—
133C4×D47—22no—
134C4×D47—42no—
135C4×D47—42no—
136C4×D47—42no—
137C4×D47—42no—
138C4×D47—42no—
139C4×D47C2×Q812yes—
140C4×D47#4112yes—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—22no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C2×D47—22no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—48no—
153C2×D47C22⋊Q812yes—
154C2×D47#13512yes—
155C2×D47AGL(1,ℤ/8)12yes—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C22×Q811yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47C22⋊Q812yes—
169C2×#478—471nomaximal, Sylow
170C2×C47—42no—
171C2×C47C2×C22⋊Q811yescharacteristic
172C2×C47C2×#13511yescharacteristic
173C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
174D47—42no—
175D47#47814yesdirect product factor
176C2×#125—471no—
177C2×C4×D4—471no—
178#478—471no—
179#478—471no—
180#478—471no—
181#478—471no—
182#478—471no—
183#478—471no—
184#478—471no—
185#478D4711yescharacteristic, direct product factor
186C2×#107—471no—
187C2×#106—471no—
188C2×C4⋊C8—471no—
189C2×#102—471no—
190C2×#102—471no—
191C47C2×#47811yescharacteristic, complemented, Sylow
192C22×D4—471no—
193C23×C4—941no—
194C22×C8—471no—
195C22×C8—471no—
196#125—471no—
197#125—471no—
198#125—471no—
199#125—941no—
200#125—941no—
201#125C2×D4711yescharacteristic, complemented
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—471no—
205C4×D4—941no—
206C4×D4—941no—
207C4×D4C2×D4711yescharacteristic
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4—941no—
213C2×C22⋊C4—941no—
214C2×C42—471no—
215#107—471no—
216#107—471no—
217#107—471no—
218#107C2×D4711yescharacteristic, complemented
219#106—471no—
220#106—471no—
221#106—471no—
222#106C2×D4711yescharacteristic, complemented
223C4⋊C8—471no—
224C4⋊C8—471no—
225C4⋊C8—471no—
226C4⋊C8C2×D4711yescharacteristic, complemented
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102C2×D4711yescharacteristic
234#102C2×D4711yescharacteristic
235C24—941no—
236C2×D4—474no—
237C2×D4—471no—
238C2×D4—942no—
239C2×D4—941no—
240C2×D4C22×D4711yescharacteristic
241C22×C4—21no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—1884no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8—942no—
255C2×C8—942no—
256C2×C8C22×D4711yescharacteristic
257C2×C8C22×D4711yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4C22×D4711yescharacteristic
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C42—471no—
280C42—471no—
281C42—471no—
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—471no—
285C23—944no—
286C23—941no—
287C23—1882no—
288C23—1882no—
289D4—21no—
290D4—472no—
291D4—944no—
292D4—941no—
293D4Q8×D4712yes—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—471no—
299C2×C4—472no—
300C2×C4—472no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4D4×D4711yescharacteristic
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—941no—
320C8—941no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—472no—
325C22—472no—
326C22—472no—
327C22—942no—
328C22—1888no—
329C22—1881no—
330C22—1881no—
331C22C2×D4×D4711yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—472no—
338C4—941no—
339C4—941no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4C2×Q8×D4711yescharacteristic
344C4#41×D4711yescharacteristic
345C2—42no—
346C2—474no—
347C2—1882no—
348C2C22⋊Q8×D4711yescharacteristic
349C2#135×D4711yescharacteristic
350C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47C2×#478
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #125×D47C2semidirect
3. #15689426C2semidirect
4. #15689425C2semidirect
5. #15689424C2semidirect
6. #15689423C2semidirect
7. #15689422C2semidirect
8. #15689421C2semidirect
9. #15689420C2semidirect
10. #107×D47C2semidirect
11. #106×D47C2semidirect
12. C4⋊C8×D47C2semidirect
15. C47×#478C2semidirect
20. #13094016C22semidirect
21. #13094015C22semidirect
22. #13094015C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. #13093955C22semidirect
43. C4⋊(C47⋊C8)C22semidirect
44. Dic47⋊C8C22semidirect
45. Dic47⋊C8C22semidirect
52. #125×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
175. D47#478direct (N × H)
185. #478D47direct (N × H)
191. C47C2×#478semidirect
201. #125C2×D47semidirect
218. #107C2×D47semidirect
222. #106C2×D47semidirect
226. C4⋊C8C2×D47semidirect